Optimizing cash flows for linear schedules modeled with singularity functions by simulated annealing

The ability of construction contractors to plan and manage cash flow is critical for their economic success. The cumulative interaction of outflows (labor, materials, and equipment costs) and inflows (progress payments less retainage) creates a profile with a complex zigzag shape. This could only be modeled by simplification, e.g., as values tabulated at discrete times; averaged S-curves without peaks; or envelopes of all possible constellations. Neither is suited for a fully integrated model that dynamically links schedules with their cash flows for optimization. Therefore, singularity functions, whose components define ranges of behavior between cutoffs, are used to flexibly yet accurately model cash flow profiles and their various payment terms. The new approach augments construction project management toward an integrated planning model and is validated with an example from the literature. Optimization with a simulated annealing algorithm shifts activity positions in a randomized but directed search for maximizing profits.